Logs

Logs are another way to write exponents
logbx=a
as an exponent b^a=x
To solve a log you have to write it as and exponent
If the log has no base than its base is 10
The base of ln is e
If b and x are equal than they cancel with the log
log M N = log M + log N
log M/N = log M – log N
log M = log N if M = N
log M^k = k log M
if there’s a log and you have to expand all the stuff in the numerator is added and all the stuff in the
denominator is subtracted
Examples
Rewrite in exponential form
1) log 1000 = 3
10^3 = 1000
2) ln 8 = 2.1
e^2.1 = 8
Expand
3) log (MN)^2
2log M + 2 log N
4) log M/(N^2)
log M – 2log N
5) log (M^2)N/(P^3)
2log M + log N – 3log P